Classifying Real Numbers

Real numbers include all the numbers on the number line, including rational numbers (like integers and fractions) and irrational numbers (like √2 and π).

A rational number is any number that can be expressed as a fraction $$\frac{a}{b}$$ , where a and b are integers and b is not zero.

An irrational number is a number that cannot be expressed as a simple fraction. Its decimal representation goes on forever without repeating.

An integer is a whole number that can be positive, negative, or zero, but does not have any fractional or decimal part.

Yes, negative numbers can be rational if they can be expressed as a fraction of two integers.

Yes, 0 is a rational number because it can be expressed as $$\frac{0}{1}$$ .

A repeating decimal has a digit or group of digits that repeat infinitely (e.g., 0.333...), while a non-repeating decimal does not (e.g., 0.5).

It is irrational because it has a non-repeating pattern.

The square root of a positive number is classified as a real number, and it can be rational or irrational depending on whether it can be expressed as a fraction.

The number π is classified as an irrational number because it cannot be expressed as a fraction.